FIG. 1 is a schematic diagram of two types of collinear ferroelectric, as are known in the art. A ferroelectric is a material which, by virtue of the material's underlying crystal structure, is able to maintain an electric polarization, or dipole moment, in the absence of an electric field. The ferroelectric may be in the form of a mono-domain 20, wherein the ferroelectric has one polarization direction, or a multi-domain 22, wherein the crystal has many domain regions, each domain having a different direction of polarization. Mono-domain ferroelectrics are well known as materials exhibiting useful properties such as piezoelectricity and electro-optical qualities. While irregular multi-domain ferroelectrics are not considered as particularly useful, multi-domain ferroelectrics where the multi-domains have a definite structure, termed domain engineered structures (DESs), have been found to have extremely useful properties.
The polarization of a single domain in collinear ferroelectrics may be in one of two directions, at 180° to each other. When a single domain is formed, the polarization of the domain will form spontaneously in one of the directions. The initial direction may be influenced during formation of the domain, for instance in a process termed poling wherein an electric field is applied as the ferroelectric material forms. Once formed, the polarization of the domain may be altered by further poling applications of the electric field. Typically, in the absence of an electric field, a multi-domain ferroelectric forms with the domains randomly oriented, giving an overall polarization close to or equal to zero, since this is the most stable energy state of the multi-domain.
FIG. 2 is a hysteresis curve for a multi-domain ferroelectric, plotting polarization P vs. electric field E, as is known in the art. As the electric field strength is increased, the domains of the ferroelectric start to align in a positive direction giving rise to a rapid increase in the overall polarization (OB). At very high field levels, the polarization reaches a saturation value (Psat), where all the multi-domains are substantially aligned in the positive direction. As the external field is reduced, the polarization reduces as some of the domains change alignment, but the polarization does not fall to zero when the external field is removed.
At zero external field, the domains remain aligned in the positive direction, hence the ferroelectric will show a remanent polarization Pr. The ferroelectric cannot be completely depolarized until a field of magnitude OF is applied in the negative direction. The external field needed to reduce the polarization to zero is termed the coercive field strength Ec. If the field is increased to a more negative value, the direction of polarization reverses, and if the field is increased sufficiently in the negative direction, the ferroelectric again reaches saturation. The value of the spontaneous polarization Ps (OS) is obtained by extrapolating the saturation curve onto the polarization axes. Ps is the polarization that the multi-domain ferroelectric would have, in the absence of an external field, if all the domains were aligned.
FIG. 3 is a schematic diagram of domain engineered structures and graphs of their properties, as are known in the art. DES 24 comprises two head-to-head domains formed in a rectangular plate of LiNbO3 with dimensions (x, y, z). A graph 26 shows the acoustic impedance vs. frequency for acoustic vibrations of DES 24. A graph 28 gives the impedance response for acoustic vibrations of a mono-domain crystal 25 of LiNbO3 having the same dimensions as DES 24, showing resonances dependent on the values of x, y and z. It is seen that these resonances are absent in DES 24. Conversely, two “bending” resonances are present in DES 24 which are not present in the mono-domain crystal.
DES 30 has a linear periodic structure where alternating domains have opposite polarizations. Structures such as DES 30 allow, for example, second harmonic generation and optical parametric oscillation for electromagnetic waves incident on the structure, because of the non-linear properties of the alternating domains of the DES. More detailed descriptions of properties and methods of production of structures such as DES 24 and DES 30 are given in an article entitled “Ferroelectric Domain Engineering for Quasi-Phase-Matched Nonlinear Optical Devices” by Rosenman, Skliar, and Arie, published in Ferroelectrics 1, N4, pp 1–64 (1998), which is incorporated herein by reference. Methods detailed therein, and others known in the art for producing domain engineered structures, are summarized below.
Domain engineered structures may be formed by altering the doping of a crystal during its growth. In an article entitled “Enhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains” by Feng et al., published in Applied Physics Letters 37, pg 607 (1980), which is incorporated herein by reference, the authors describe a method for varying the spontaneous polarization of growing LiNbO3 crystals by changing the doping of the crystals. The doping was changed by periodically altering the temperature of the growing crystal, which in turn altered the concentration of yttrium which was used to dope the crystals. The variation in yttrium concentration caused a periodic reversal of the polarization of the crystals, the reversal appearing through the bulk of the crystals.
Diffusion at relatively high temperatures can be used to form DESs. For example, in an article entitled “Balanced phase matching in segmented KTiOPO4 waveguides” by Bierlein et al., published in Applied Physics Letters 56, pg 1725 (1990), which is incorporated herein by reference, the authors describe polarization in KTiOPO4 (KTP) crystals. By immersing the KTP crystals in molten RbNO3/Ba(NO3)2, at a temperature of about 350° C. for approximately 1 hour, Rb+ ions exchanged with K+ ions of the KTP. The presence of the Ba2+ ions caused polarization inversion of domains at the surface of the KTP. It will be appreciated that diffusion induced DESs are substantially surface structures.
Electron beam writing may be used to form DESs. For example, in an article entitled “Fabrication of Domain Reversed Gratings FOR SHG in LiNbO3 by Electron Beam Bombardment” by Keys et al., published in Electronics Letters 26, pg 188 (1990), which is incorporated herein by reference, the authors describe domain polarization reversal on the negative face of a LiNbO3 crystal. It will be appreciated since the electron beams penetrate no more than some microns in depth, DESs produced by electron beam writing must be of this order of thickness.
FIG. 4 is a schematic diagram of a poling system for fabrication of DESs, as is known in the art. A mono-domain ferroelectric 40 has a periodic dielectric photo-resist 42 applied to an upper surface of the ferroelectric. A first conductor 44 is overlaid on photo-resist 42 and the upper surface, and a second conductor 46 is applied to a lower surface of the ferroelectric. A high-voltage pulse is applied between the two electrodes. The pulse reverses the polarization of the ferroelectric in regions where the first conductor contacts the ferroelectric. This technique, and similar ones using liquid electrodes, have been used to form periodic DESs having thicknesses in a range of 0.5–3 mm, and with periods between 3.4 and 39 microns.
Scanning force microscopy (SFM) is a method known in the art for imaging surfaces, and also for modification of domain structures of thin films of ferroelectrics. A review of SFM is provided in an article entitled “Nanoscale Scanning Force Imaging of Polarization Phenomenon in Ferroelectric Thin Films” by Auciello et al., published in The Annual Review of Material Sciences 28, pgs 33–41 (1998), which is incorporated herein by reference. The review includes a description of contact and non-contact SFM. In both types of SFM, a tip-electrode is scanned across the surface of a sample to be imaged, and forces exerted on the tip by the sample enable ferroelectric domains within the sample to be imaged.
FIG. 5 is a schematic diagram of a scanning force microscope (SFM) 50, as described in an article entitled “Ferroelectric domain switching in tri-glycine sulphate and barium-titanate bulk crystals by scanning force microscopy” by Eng et al., published in Applied Physics A 66, S679–S683 (1998), which is incorporated herein by reference. In the article the authors describe how microscope 50 may be used to form DESs. A tip-electrode 52, supported by a cantilever 62, is scanned relative to an upper surface 54 of a ferroelectric sample 56. Tip-electrode 52 ends in an extremely sharp point, so that very high electric fields are generated at the tip. The height of tip-electrode 52 above the surface is maintained at a substantially fixed distance, of the order of nanometers, by circuitry 58. Circuitry 58 comprises a function generator 64 which provides an alternating potential U1 of amplitude 10 V and frequency 20 kHz that is applied to the tip-electrode, causing cantilever 62 to oscillate vertically. The vertical oscillations of the cantilever are detected by a 2-quadrant photo-detector 51, which receives a laser beam after reflection from the cantilever. An output of the photo-detector is input to an amplifier 53, which outputs a negative feedback signal to a z-positioner 55.
Sample 54 is supported on a counter-electrode 60, which may be set to a potential U2 of 60 V for a certain exposure time τ, enabling domain-forming electric field pulses to be applied to sample 56. Using this technique, DESs having a lifetime of more than 5 days were formed in 125 micron thick BaTiO3. However, in 700 micron thick tri-glycine sulphate (TGS), the domains had a lifetime of only 30 minutes.
In chapter 4 of Principles and Applications of Ferroelectric and Related Materials, by Lines et al., published by The Clarendon Press, Oxford (1977), which is incorporated herein by reference, the authors describe a three-stage process for the production of a ferroelectric domain in a ferroelectric material which is already spontaneously polarized. This process also leads to the formation of domains in the scanning process of SFM 50. In a first stage, a nucleus of a primary domain is formed by an applied field opposite in direction to the spontaneous polarization. A local value of the applied field must be larger than a coercive field of the material. In a second stage, the nucleus grows in a forward and sideways direction. In a third stage, secondary domain nuclei generate at the domain wall of the primary nucleus.
An important consideration in domain reversal phenomenon is domain configuration stability. In an article entitled “Switching kinetics of 180° domains in congruent LiNbO3 and LiTaO3 crystals” by Gopalan et al., published in Solid State Communications, 109, 111 (1999) which is incorporated herein by reference, the authors describe how the stabilization process may be related to pinning of the domain wall by randomly distributed defects of different origin. A corresponding characteristic time for the stabilization process is determined by the time needed for the equilibrium distribution of local pinning (defect) centers around the domain walls. (A similar process occurs with Cottrell clouds.) Thus, in order to stabilize the reversed domains, the applied voltage pulse duration should be longer than the stabilization process occurring in the domain pinning process.
A switching time τsw for complete reversal of the initial spontaneous polarization is thus given byτsw=τnucl+τforw+τstab  (1)wherein τnucl is a time for the primary domain nucleus to be formed, τforw is a time for the forward/sideways growth to occur, and τstab is a stabilization time needed for full pinning of a reversed domain.
The authors of Principles and Applications of Ferroelectric and Related Materials describe a method using pulsed polarization reversal for evaluating τsw. (The method is described in more detail in chapter 7 of Ferroelectricity by Fatuzzo and Merz, published by North-Holland Publishing Company (1967), which is incorporated herein by reference.) The method may also be used to produce a DES, and it is stated that for complete polarization reversal, a duration τdur of a DC pulse generating the DES must satisfy the following equation:τdur>τsw  (2)
Providing that equation (2) is satisfied, no back-switching effect or instability is present in the formed DES.
Hereinbelow the terms zero-dimensional, one-dimensional, and two-dimensional are used in referring to a DES. It will be understood that the terms refer to respective cross-sections of the DES, so that a zero-dimensional DES comprises generally rod-like structures, a one-dimensional DES comprises generally plate-like structures, and a two-dimensional DES comprises generally prism-like structures.